Wendel's theorem

In geometric probability theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an

In other words, one seeks the probability that there is some half-space with the origin on its boundary that contains all N points.

Wendel's theorem says that the probability is[1] The statement is equivalent to

being the probability that the origin is not contained in the convex hull of the N points and holds for any probability distribution on Rn that is symmetric around the origin.

This is essentially a probabilistic restatement of Schläfli's theorem that